Now, generally many slot machines, which execute a reel game, are installed in casinos. In these slot machines, there exist many machines, which execute a game including a primary game and a free spin game. Since the free spin game is usually carried out as a bonus game of the primary game, the free spin game is set up so that higher prizes may be paid to a player, and is positioned as a game, which further excites a player. However, the conventional free spin game was performed in a form just like a primary game, and it had the feature that winning combination appears with high probability. However the free spin game is insufficient as a position of a bonus game, and it has not excited players enough. An appearance of a secondary game, such as a free spin game, which can excite players more under such a status, has been desired.